Coalescence is the problem of isolated mobile robots independently searching for peers with the goal of forming a single connected network. We are interested in coalescence time for a scenario where the robots do not have any information about the environment or positions of other robots and perform a random search. In an earlier work, we analyzed a simple case where robots coalesce on hitting a stationary base station and showed through analysis and simulations that the coalescence time decreases as O(1/sqrt(N)), where N is the size of the network. In this paper, we consider the general case where there is no stationary base station and robots coalesce when they hit other robots. The coalescence time in this case is bounded from above by 1/sqrt(N) and from below by log(N)/N. Simulations suggest that the lower bound is tight.